A family with three children is randomly selected. Assume that births of boys and girls are equally likely. Construct a
Table showing the probability distribution for the events 3 girls, 2 girls, 1 girl, and 0 girls.

$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&\text { Probability }\
\hline \
\
\
\
\hline\text { Total }
\end{array}$

A)
$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&\text { Probability }\
\hline 3 \text { girls } & 0 \text { boys } \
2 \text { girls } & 1 \text { boy } \
1 \text { girl } & 2 \text { boys } \
0 \text { girls } & 3 \text { boys }\
\hline\text { Total }&8
\end{array}$

B)
$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&&\text { Probability }\
\hline3 \text { girls } & 0 \text { boys } & 1 \
2 \text { girls } & 1 \text { boy } & 1 \
1 \text { girl } & 2 \text { boys } & 1 \
0 \text { girls } & 3 \text { boys } & 1 \
\hline\text { Total }&&4
\end{array}$

C)
$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&&\text { Probability }\
\hline3 \text { girls } & 0 \text { boys } & 1 / 8 \
2 \text { girls } & 1 \text { boy } & 3 / 8 \
1 \text { girl } & 2 \text { boys } & 3 / 8 \
0 \text { girls } & 3 \text { boys } & 1 / 8\
\hline\text { Total }&&1
\end{array}$

D)
$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&&\text { Probability }\
\hline3 \text { girls } & 0 \text { boys } & 1 / 4 \
2 \text { girls } & 1 \text { boy } & 1 / 4 \
1 \text { girl } & 2 \text { boys } & 1 / 4 \
0 \text { girls } & 3 \text { boys } & 1 / 4\
\hline\text { Total }&&1
\end{array}$

Question

A family with three children is randomly selected. Assume that births of boys and girls are equally likely. Construct a
Table showing the probability distribution for the events 3 girls, 2 girls, 1 girl, and 0 girls.

$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&\text { Probability }\
\hline  \
\
 \
\
\hline\text { Total }
\end{array}$

A)
$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&\text { Probability }\
\hline 3 \text { girls } & 0 \text { boys } \
2 \text { girls } & 1 \text { boy } \
1 \text { girl } & 2 \text { boys } \
0 \text { girls } & 3 \text { boys }\
\hline\text { Total }&8
\end{array}$

B) 
$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&&\text { Probability }\
\hline3 \text { girls } & 0 \text { boys } & 1 \
2 \text { girls } & 1 \text { boy } & 1 \
1 \text { girl } & 2 \text { boys } & 1 \
0 \text { girls } & 3 \text { boys } & 1 \
\hline\text { Total }&&4
\end{array}$

C) 
$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&&\text { Probability }\
\hline3 \text { girls } & 0 \text { boys } & 1 / 8 \
2 \text { girls } & 1 \text { boy } & 3 / 8 \
1 \text { girl } & 2 \text { boys } & 3 / 8 \
0 \text { girls } & 3 \text { boys } & 1 / 8\
\hline\text { Total }&&1
\end{array}$

D)
$\quad $ $\quad $$3 \text { Child Family }$
$\begin{array}{cc}
\hline \text { Result }&&\text { Probability }\
\hline3 \text { girls } & 0 \text { boys } & 1 / 4 \
2 \text { girls } & 1 \text { boy } & 1 / 4 \
1 \text { girl } & 2 \text { boys } & 1 / 4 \
0 \text { girls } & 3 \text { boys } & 1 / 4\
\hline\text { Total }&&1
\end{array}$

Quizplus · Accepted Answer

The probabilities are calculated based on the binomial distribution, with each child having a 1/2 chance of being a girl or a boy. For 3 girls (or 0 boys), the probability is (1/2)^3 = 1/8. For 2 girls and 1 boy (or vice versa), there are 3 ways this can happen (GBB, BGB, BBG for boys and GGG, GGB, GBG, BGG for girls), each with a probability of (1/2)^3, making the total probability 3*(1/2)^3 = 3/8. The total probability sums up to 1, confirming the distribution is correct.

A Family with Three Children Is Randomly Selected \quad \quad

A Family with Three Children Is Randomly Selected $\quad$ $\quad$